Pc_givena:
Probability of observing the ith nearest neighbour at distance greater or equal c given the (i-1)th nearest neighbour at distance a
Description
This function gives the probability of observing the ith nearest neighbour at distance c given the (i-1)th nearest neighbour at distance a, $P(d_i >= x | d_(i-1) = a)$
Usage
Pc_givena(i, c, a, N)
Arguments
i
numeric, which nearest neighbour to consider
c
vector, the distance at which the ith NN was observed
a
vector, the distance at which the (i-1)th NN was observed, a
N
numeric, size of the dataset
Value
Probability vector
Details
The probability is calculated by ranking the data and assuming that the data lie on a torus. For details see Dümcke et al. "A novel test for independence derived from an exact distribution of ith nearest neighbours" (manuscript in preparation)